An efficient contact algorithm for the interaction of material particles with finite elements

In this paper, we propose an efficient contact algorithm to analyze the interaction of material particles with finite elements. The contact forces between material particles and finite elements are computed at the (background) grid nodes in material point method, and transferred to finite element nodes. A weighted average method is used to obtain the velocities at grid nodes contributed from finite element nodes, and a cut-off weight is applied to the contact condition to avoid an early contact occurring in a grid-based contact algorithm. A severe penetration of material particles into finite elements when the finite element mesh is coarser than the background grid can be prevented by introducing distributed interaction (DI) nodes on the contact faces of finite elements. Numerical examples show the effectiveness of the present method to treat the contact interaction between material particles and finite elements.